We construct a new discrete analog of the Dirac-K\"{ a}hler equation in which some key geometric aspects of the continuum counterpart are captured. We describe a discrete Dirac-K\"{ a}hler equation in the intrinsic notation as a set of difference equations and prove several statements about its decomposition into difference equations of Duffin type. We study an analog of gauge transformations for the massless discrete Dirac-K\"{ a}hler equations.
Categories: math-ph math.AP math.MP